In a conventional serial data system, symbols are transmitted sequentially, with the frequency spectrum of each data symbol allowed to occupy the entire bandwidth. A parallel data transmission system is one in which several sequential streams of data are transmitted simultaneously. In a parallel system, the spectrum of an individual data element normally occupies only a small part of the available bandwidth.
In a classic parallel data system, the total signal frequency band is divided into N overlapping frequency subchannels. Each subchannel is modulated with a separate symbol. The subchannels are then multiplexed.
Orthogonal signals can be separated at the receiver by using correlation techniques, eliminating inter-symbol interference. This can be achieved by carefully selecting carrier spacing so as to let the carrier spacing equal the reciprocal of the useful symbol period. Orthogonal Frequency Division Multiplexing (OFDM) is a form of multicarrier modulation wherein carrier spacing is selected so that each subcarrier is orthogonal to the other subcarriers.
This orthogonality avoids adjacent channel interference and prevents the demodulators from seeing frequencies other than their own. The benefits of OFDM are high spectral efficiency, resiliency to Radio Frequency (RF) interference, and lower multi-path distortion.
In OFDM the subcarrier pulse used for transmission is chosen to be rectangular. This has the advantage that the task of pulse forming and modulation can be performed by a simple Inverse Discrete Fourier Transform (IDFT) which can be implemented very efficiently as an Inverse Fast Fourier Transform (IFFT). Therefore, the receiver only needs a FFT to reverse this operation.
Incoming serial data is first converted from serial to parallel and grouped into x bits each to form a complex number. The number x determines the signal constellation of the corresponding subcarrier, such as 16 Quadrature Amplitude Modulation. The complex number are modulated in a baseband fashion by the IFFT and converted back to serial data for transmission. A guard symbol is inserted between symbols to avoid inter-symbol interference (ISI) caused by multi-path distortion. The discrete symbols are converted to analog and low-pass filtered for RF up-conversion. The receiver then simply performs the inverse process of the transmitter.
According to the theorems of the Fourier Transform the rectangular pulse shape will lead to a sin(x)/x type of spectrum of the subcarriers, as illustrated in FIG. 1. The spectrums of the subcarriers are not separated but overlap. The reason why the information transmitted over the carriers can be separated is the orthogonality relation. By using an IFFT for modulation, the spacing of the subcarriers is chosen such that at the frequency where a received signal is evaluated (indicated by letters A-E in FIG. 1) all other signals are zero.
The seminal article on OFDM is “Data Transmission by Frequency-Division Multiplexing Using the Discrete Fourier Transform”, by S. B. Weinstein and Paul M. Ebert in IEEE Transactions on Communication Technology, Vol. com-19, No. 5, October 1971, the contents of which are hereby incorporated by reference.
OFDM forms the basis for the Digital Audio Broadcasting (DAB) standard in the European market as well as the basis for the global Asymmetric Digital Subscriber Line (ADSL) standard. Development is ongoing for wireless point-to-point and point-to-multipoint configurations for Wireless Local Area Networks using OFDM technology. In a supplement to the IEEE 802.11 standard, the IEEE 802.11 working group published IEEE 802.11a, which outlines the use of OFDM in the 5.8-GHz band.
A packet communication system, similar to other types of communication systems, provides for the communication of data between communication stations within a set of communication stations. The set includes at least a sending station and a receiving station. Data originated at, or otherwise provided to, a sending station is caused to be communicated by the sending station for delivery at a receiving station. The data sent by the sending station is sent upon a communication channel, and the receiving station monitors the communication channel, thereby to detect delivery of the data communicated thereon.
In a packet communication system, data that is communicated is first packetized into packets of data, and the data packets, once formed, are then communicated, sometimes at discrete intervals. Once delivered to a receiving station, the information content of the data is ascertained by concatenating the information parts of the packets together. Packet communication systems generally make efficient use of communication channels as the communication channels need only to be allocated pursuant to a particular communication session only for the period during which the data packets are communicated. Packet communication channels are sometimes, therefore, shared communication channels that are shared by separate sets of communication stations between which separate communication services are concurrently effectuated.
Operating specifications that define the operating protocols of various types of packet radio communication systems have been promulgated and yet others are undergoing development and standardization. A packet radio communication system provides the advantages of a radio communication system in that the communication stations that are parties to a communication session need not be interconnected by electrically-conductive connectors. Instead, the communication channels of a packet radio communication system are formed of radio channels, defined upon a portion of the electromagnetic spectrum.
While packet radio communication systems have been developed for the effectuation of various different types of communication services, much recent interest has been directed towards the development of packet radio communication systems capable of providing data-intensive communication services. For instance, the IEEE 802.15.3a operating specification contemplates an OFDM Ultra Wide Band (UWB) communication system, capable of communicating data over wide bandwidths over short ranges.
A structured data format is set forth in the present promulgation of the operating specification. The data format of a data packet formed in conformity with the IEEE 802.15.3a includes a preamble part and a payload part. Other packet communication systems analogously format data into packets that also include a preamble part and a payload part. The payload part of the packet contains the information that is to be communicated. That is to say, the payload part is nondeterminative. Conversely, the preamble part of the data packet does not contain the informational content that is to be communicated but, rather, includes determinative data that is used for other purposes. In particular, the preamble part of an IEEE 802.15.3a packet preamble includes three parts, a packet sync sequence, a frame sync sequence, and a channel estimation sequence. The packet sync sequence is of a length of twenty-one OFDM (symbols), the frame sync sequence is of a length of three OFDM symbols, and the channel estimation sequence is of a length of six OFDM symbols. Collectively, the sequences are of a time length of 9,375 microseconds.
The preamble portions are used, for instance, to facilitate synchronization between the sending and receiving stations that send and receive the data packet, respectively. Additionally, the preamble is used for purposes of automatic gain control (AGC). For use of automatic gain control, a receiving station is able to set its gain at an appropriate level, e.g., to facilitate application of received data to an analog-to-digital converter to supply useful bits to a baseband part of the receiving station.
The preamble is further used for purposes of packet detection. Packet detection identifies to the receiving station the reception at the receiving station of the packet. Upon detection of the packet, e.g., various state machines at the receiving station are started to enable processing of the incoming packet.
Of particular significance, the preamble also is used for channel estimation. The radio channel upon which the packet is communicated undergoes reflections and is otherwise distorted during its communication to the receiving station. To receive the transmitted data correctly, the receiving station must be provided with a good estimate of the channel to permit proper compensation to be made of the channel. The channel estimation sequence is a known wave form that tells the receiver what the channel looks like. From this known wave form, the receiver can properly extrapolate unknown sequences.
The PAR is the ratio of the instantaneous peak value (maximum magnitude) of a signal parameter to its time-averaged value. Unfortunately, high PAR signals tend to increase the resolution requirements of receive and transmit converters to reduce clipping, which in turn increases power consumption and cost. Lowering the PAR allows for lower power consumption and fewer bits in Analog-to-Digital (A/D) and Digital-to-Analog (D/A) converters.
During the channel estimation sequence, the multipath channel response is estimated. While clipping in the packet synchronization, frame synchronization or data portion of the packet can be tolerated to an extent, it is very important to avoid clipping the channel estimation sequence. Errors in the channel estimation sequence have a forward propagation effect because the channel estimate is used to decode all the data following the channel estimation sequence. This forward propagation effect raises the noise floor on all data, decreasing the probability of a successful packet transfer.
Unfortunately, OFDM signal tends to have a high PAR. For sequences such as channel estimation sequences, it is desirable to find sequences that yield low PAR. To lower the probability of clipping the channel estimation sequence, a deterministic training sequence is used. It is desirable to find sequences with very low PAR that are well below the average of random sequences. However, the space of all sequences is too large to search. In the multiband specification, the training sequence is of length 122 bits. There are 4122 possible quadrature-phase-shift-keyed (QPSK) sequences of this length. Thus it is clear that an exhaustive search to find the lowest PAR sequence is practically impossible.
The search for low PAR sequences has historically been performed by random search. Since the space of all sequences is very large, the whole space cannot be searched. Thus the best sequence is typically not found.
Therefore, it would be desirable to have a method for identifying the best low PAR sequences without randomly searching the whole space of sequences.